X.
Prof. K. U. Ingard
Dr. L. W. Dean III
Dr. R. G. Chatterji
A.
A LOW RESONANT
PHYSICAL ACOUSTICS
E. J. Martens, Jr.
D. S. Wiley
H. L. Willke, Jr.
N. A. Ball
G. C. Maling, Jr.
FREQUENCY BARIUM TITANATE TRANSDUCER
A barium titanate slab with a resonant frequency of 1000 cps would be 2. 5 meters
thick.
Therefore, if one wants a resonant transducer at lower frequencies,
one must
find some way to lower the resonant frequency of a piece of barium titanate of reasonable
dimensions.
One approach to the problem is the configuration shown in Fig. X-1.
barium titanate are cemented together to form a bilaminate,
is applied across the faces.
Two strips of
which bends when a voltage
The resonant frequency is lowered by the addition of masses
Transducers having resonant frequencies from 100 cps to 2000 cps were
made from barium titanate bilaminates 6 cm long, 3 cm wide, and 1/3-1 cm thick by
to the ends.
adding end masses of approximately 100-200 grams.
TITANATE CERAMIC
BARIUM
(BILI
NATE)
E-ELECTRICAL CONI:ECTIONS
TO SILVERD FACES
OF CERAMIC
Fig. X-1.
A mass-loaded bar.
Attempts to find a simple formula relating the resonant frequency to the transducer
parameters have failed. However, by adding or subtracting mass from the ends, the
device can be tuned to a particular frequency.
Since the transducer is physically much smaller than a wavelength of sound at its
resonance, it does not make an efficient radiator. For such a device the radiation
impedance of various media does not scale as pc, where p is the density, and c the
4,
where k is the wave number (k=w/c), and a is a charspeed of sound, but as pc - (ka)
acteristic dimension of the transducer.
water than it is in air.
Thus this device is a less efficient radiator in
The radiation pattern, as expected, is that of a dipole, the axis
This work was supported in part by the U. S. Navy (Office of Naval Research) under
Contract Nonr-1841(42).
131
(X.
PHYSICAL ACOUSTICS)
of which is perpendicular to the flat surface of the bilaminate.
Details of measurements of the electrical and mechanical parameters are given
in N. A. Ball's thesis. 1
N. A. Ball, L. W. Dean III
References
1. N. A. Ball, Determination of Design Parameters for a Novel Electroacoustical
Transducer, S. M. Thesis, Department of Electrical Engineering, M. I. T. , June 1961.
B.
THE DAMPING OF MECHANICAL OSCILLATORS BY FLOW
A low-speed wind tunnel has been constructed in order to make measurements on
the damping of mass-spring oscillators by flow. The damping of an oscillator has been
found to be a strong function of flow velocity. For example, the amplitude of an oscillator with a period of 1. 04 seconds decreases to one-half of its original value with no
flow in 6 minutes and 37 seconds. A flow velocity of 200 feet per minute past the mass
causes this damping time to decrease to 1 minute and 27 seconds.
Results of this kind can be most easily interpreted by using the following analysis:
The force on the mass is
F = K(V-u) ,
(1)
where V is the air stream velocity, u is the velocity of the mass, and K is some proportionality factor. In practice, u can be made much less than V so that, apart from
a steady force that shifts the equilibrium position slightly, the drag force may be written
F = 2KVu.
(2)
The drag force is therefore proportional to the oscillator velocity and should result
in ordinary exponential damping. The dependence (if any) of K on oscillator frequency
and flow speed can be found by measurement of the damping time. The experiments
that have been performed, thus far, have not given particularly satisfactory results
because disk-shaped weights were used to change the mass, and therefore the period
of the oscillator. In the next series of experiments, the mass will be a sphere, and
the period will be changed by changing the spring constant.
U. Ingard, G. C. Maling, Jr.
C.
ACOUSTICS OF INHOMOGENEOUS MOVING MEDIA
Two problems that involve acoustic wave propagation in inhomogeneous media are
being investigated. The first involves the effect of a plane boundary on the magnitude
132
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PHYSICAL ACOUSTICS)
of the fluctuations in sound pressure that occur when a slowly moving turbulent air
stream is made to pass over the boundary.
This problem has been analyzed theoretically and an experiment is now being carried
out in the anechoic chamber to study the problem further. Construction of the experimental apparatus has now been completed and data are being obtained.
Another aspect of the interaction of sound with moving air streams involves the influence of a heat source in a moving medium. Through the modulation of the heat transfer
to the medium by the sound itself, the heat source acts as a scatterer of sound. The
conditions for self-sustained oscillations (as in the Rijke tube) are being investigated
with particular emphasis on the amplitude of the oscillations as a function of geometry,
heat-source parameters, and so forth. The effect has been observed in a number of
Rijke tubes of various sizes, but quantitative data have not yet been obtained because
of difficulties involved in the construction of a heat source that will introduce heat into
the medium at a known rate.
G. C. Maling, Jr.
D.
BIFURCATION INSTABILITY OF A LIQUID CONDUCTOR IN AN AXIAL
MAGNETIC FIELD*
During the past year, an extensive series of experiments has been performed to
study the instability of a mercury current filament moving in an axial constant magnetic
Fig. 2.
*This work was
Grant G-9330.
Illustration of self-pinch of a mercury
column falling freely under gravity,
and carrying a current of 180 amp.
The diameter of the mercury column
is 0. 3 cm.
supported in part by the National Science
133
Foundation under
Fig. X-3.
Illustration of spiral instability of a mercury column falling
under gravity in an axial magnetic field. The diameter of
the mercury column is 0. 5 cm; the electrical current through
it, 80 amps; and the axial magnetic field, 2200 gauss. Notice
that the cross section of the mercury column is deformed
as it spirals and that there is an indication of bifurcation.
Actually, judging from the reflected light pattern at point P,
two indentations seem to be present in the stream.
Fig. X-4.
134
Illustration of a fully developed
bifurcation resulting from spiral
instability in a mercury column
moving in an axial magnetic field.
The diameter of the column is
0. 5 cm; the current through it,
260 amps; and the magnetic field,
3600 gauss.
(X.
field.
PHYSICAL ACOUSTICS)
The pinch instability of this mercury filament (with no magnetic field present),
and the spiral instability, have been studied and photographed by means of high-speed
photography. A typical example of pictures showing pinch and spiral instabilities is
shown in Figs. X-2 and X-3.
During the course of these studies a new type of instability
was found which might be referred to as a "bifurcation instability," and is illustrated
in the photograph in Fig. X-4. At sufficiently large magnetic fields it was found that
the mercury stream divides in two, continuing to spiral about the magnetic field.
This
bifurcation results presumably from the fact that when the mercury column bends, its
cross section changes from circular to elliptical, and this distortion of the cross section continues until the stream divides in two.
A detailed account of these experiments
is being prepared for publication.
D. S. Wiley, U.
E.
Ingard
SEARCH FOR A STABLE PINCH IN A HORIZONTAL MERCURY COLUMN
In the first published account1 of the pinch phenomenon in a liquid conductor, and
in a later systematic study of this phenomenon, it was indicated that a stable pinch can
be obtained in a horizontal mercury column that is carrying an electric current. This
pinch, which formed a V-shaped indentation on the free surface of the mercury, was
claimed to be stable and to increase in depth with the current. A theoretical study of
this problem has been undertaken, and it has been shown that, at least for an infinitely
Experiments have been
long horizontal mercury column, a pinch cannot be explained.
performed to study this phenomenon by using a mercury column in a vertical tray consisting of lucite plates. The thickness of the column was approximately 0. 5 inch, the
length was approximately 10 inches, and the height was varied from 0. 5 inch to 3 inches.
Currents up to 2000 amps were used. No pinches were found. Pinchlike deformations
of the free surface of the mercury could be obtained, however, if the electric leads to
the column were asymmetrical and hence produced asymmetry in the magnetic field,
and it is clear that in experiments of this type special care should be taken to avoid
inhomogeneities in the magnetic field. When such inhomogeneities are produced intentionally by ferromagnetic materials placed above the mercury columns,
steady defor-
mations of the free-mercury surface are readily produced.
U. Ingard, D. S. Wiley
References
1. C. Hering, A practical limitation of resistance furnaces, the Pinch Phenomenon,
Trans. Am. Electrochem. Soc., Vol. XI, p. 329, 1907.
*This
work
was
supported in
part by the
Grant G-9330.
135
National
Science
Foundation
under
(X.
PHYSICAL ACOUSTICS)
2. E. E. Northrup, Some newly observed manifestations of forces in the interior
of an electric conductor, Phys. Rev. 24, 474 (1907).
F.
OSCILLATION OF A FERROMAGNETIC
BODY INSIDE A LIQUID CONDUCTOR
In the course of our studies of instabilities of a mercury column, an amusing effect
was found by floating a piece of metal on the surface of a horizontal mercury column.
When a current (of approximately 1000 amps) was sent through the column, the piece
of iron was pulled into the mercury and set into vertical oscillations approximately about
the center of the mercury column.
At the center of the column the magnetic field is
clearly zero and the vertical field gradients on either side are directed toward the center
line, thereby producing a linear restoring force on the piece of iron.
U.
This work
Grant G-9330.
was
supported
in
part by the
136
National
Science
Ingard, D. S. Wiley
Foundation
under